 2.5.1: Complete parts ac for each set of data in Exercises 1 and 2. a. Dra...
 2.5.2: Complete parts ac for each set of data in Exercises 1 and 2. a. Dra...
 2.5.3: All states and the District of Columbia have enacted laws setting 2...
 2.5.4: The table shows the number of goals and assists for some of the mem...
 2.5.5: The table shows the number of gallons of bottled water consumed per...
 2.5.6: The table shows the total revenue of all Broadway plays for recent ...
 2.5.7: Write a prediction equation from the data for 1999 to 2003.
 2.5.8: Use your equation to predict the amount for 2014.
 2.5.9: Compare your prediction to the one given in the graph.
 2.5.10: Based only on these data, which stock should Della buy? Explain
 2.5.11: Do you think investment decisions should be based on this type of r...
 2.5.12: Draw a scatter plot with average distance as the independent variable
 2.5.13: Write a prediction equation
 2.5.14: Predict the average temperature for Neptune, which has an average d...
 2.5.15: Compare your prediction to the actual value of 330F
 2.5.16: Use the Internet or other resource to look up the population of you...
 2.5.17: Use a prediction equation to predict the percent in 2015.
 2.5.18: Do you think your prediction is accurate? Explain.
 2.5.19: Write a different prediction equation for the data in the example o...
 2.5.20: Use the information on page 86 to explain how a linear equation can...
 2.5.21: Which line best fits the data in the graph?
 2.5.22: Anna took brownies to a club meeting. She gave half of her brownies...
 2.5.23: Write an equation in slopeintercept form that satisfies each set o...
 2.5.24: Write an equation in slopeintercept form that satisfies each set o...
 2.5.25: Write a linear equation to model this situation.
 2.5.26: How much would it cost to talk for half an hour at the night rate?
 2.5.27: Find the slope of the line that passes through each pair of points
 2.5.28: Find the slope of the line that passes through each pair of points
 2.5.29: Find the slope of the line that passes through each pair of points
 2.5.30: Kara is planning to set up a booth at a local festival to sell her ...
 2.5.31: Find each absolute value
 2.5.32: Find each absolute value
 2.5.33: Find each absolute value
 2.5.34: Find each absolute value
 2.5.35: Find each absolute value
Solutions for Chapter 2.5: Statistics: Using Scatter Plots
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter 2.5: Statistics: Using Scatter Plots
Get Full SolutionsChapter 2.5: Statistics: Using Scatter Plots includes 35 full stepbystep solutions. This textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. California Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568. Since 35 problems in chapter 2.5: Statistics: Using Scatter Plots have been answered, more than 44636 students have viewed full stepbystep solutions from this chapter.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B IIĀ·

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.